In modern storage technology and communication technology, due to its intrinsic physical feature, the channel may produce constrains in a certain form to the channel-passing signal. In order to reduce the effect of the channel on the signal, and improve the reliability of the storage system and communication system, one of the methods to solve this problem is to use limited encoding technique, wherein limited encoding is also called modulation encoding. It is represented by (d, k) run-length limited (RLL), in which d is a minimum run length and k is a maximum run length of “0” between consecutive 1's. The famous Miller Code, also known as Modified Frequency Modulation (MFM) (U.S. Pat. No. 3,108,261, issued on Oct. 22, 1963) is a typical representative. In MFM code, between adjacent 1's, the run length of “0” is at least 1, and at most 3, thus MFM code sometimes is also called one-dimensional (1, 3) RLL code.
With the development of technique, a new-type memory stored in the two-dimensional page form makes its appearance in recent years, e.g. holographic memory and two-dimensional CD. One of the greatest differences between these memories and the popular memories lies in that the data are stored on the recording medium in the two-dimensional page form for each time, and they are read also page by page. FIG. 1 is the schematic for such two-dimensional layout for data in a holographic memory.
In the above two-dimensional memory, taking FIG. 1 as the example, if the influence of boundary is not considered, the bit information for each digit will have 4 bit information which is directly adjacent to itself (usually up, down, left and right). By comparison, the data layout will be shown as FIG. 2 in the one-dimensional case.
As can be seen in FIG. 1 and FIG. 2, in two-dimensional storage, the binary data array has constraint both in horizontal and vertical directions. For this reason, the previously-mentioned Modified Frequency Modulation (MFM) will have its intrinsic constraint between data changing accordingly with the space dimension from one dimension to two dimensions, and the constraint previously satisfied under one-dimensional conditions will lose its effect under two-dimensional conditions. In this connection, it is extremely necessary to seek new two-dimensional limited encoding/decoding methods, as to ensure the data in horizontal and vertical directions both satisfying the development and demand of a new two-dimensional storage technique.